The son of a treasury official, Köchel took a doctorate in law at the University of Vienna in 1827. He then held a series of positions as private tutor to noble families, most notably from 1827 to 1842 in tutoring the four sons of Archduke Karl. His colleague in this pursuit was Dr. Franz von Scharschmied, who became his lifelong companion. After being knighted for his services in 1842, Köchel lived mostly on his inheritance and joined Scharschmied in the latter’s official travels as tax assessor.

Köchel developed a considerable reputation in botany and mineralogy but from about 1851 devoted himself especially to music and the work of Mozart. He worked for about a decade to produce his great catalog, Chronologisch-thematisches thematisches Verzeichnis sämtlicher Tonwerke Wolfgang Amade Mozarts (1862; “Chronological Thematic Catalog of the Collected Musical Works of Wolfgang Amadeus Mozart”). Unlike most other later composers, Mozart did not enumerate his works with a consecutive set of opus numbers, and he had not always dated his compositions; as a result, there had been a great deal of confusion as to the order and period of his many works. Köchel set himself to bring order out of this chaos. To make his catalog, Köchel used a list that Mozart himself had compiled of his works from 1784. An imperfect catalog by Aloys Finch (1837) and a publication based on Mozart’s autograph scores by Johann Anton André (1828) were also available to Köchel. Köchel classified the hundreds of unnumbered Mozart compositions into 23 categories and, on the basis of stylistic development and Mozart’s musical handwriting, assigned a date of composition to each work. Köchel’s listings of Mozart’s authentic works extend from K 1 (minuet for piano, 1762) to K 626 (Requiem Mass, 1791). Subsequent editions—by P. von Waldersee (1905), Alfred Einstein (1937), and Franz Giegling (1964)—greatly added to Köchel’s store of information and radically revised the numbering of some pre-1784 works (for which the designations “K-E” or “K6” are now commonly sometimes used).

Two years before his death Köchel instigated and subsidized the publication of the Breitkopf and Härtel complete edition of Mozart’s works (1877–1905).